Malliavin calculus for regularity structures: The case of gPAM

Malliavin calculus is implemented in the context of Hairer (2014) [16]. This involves some constructions of independent interest, notably an extension of the structure which accommodates a robust, and purely deterministic, translation operator, in $L^2$-directions, between “models”. In the concrete context of the generalized parabolic Anderson model in 2D – one of the singular SPDEs discussed in the afore-mentioned article – we establish existence of a density at positive times.     

Stokes constants of an oblate ellipsoid of revolution with equidensites homothetic to its surface

The theory of equilibrium figures was actively developed in the 19th century, when it was found that the observed massive celestial bodies (the Sun, planets, and satellites) had an almost ellipsoidal form. The existence of exactly ellipsoidal figures was also established. The gravitational potential of these figures is represented by a Laplace series with its coefficients (Stokes’ constants I _n ) determined by some integral operator. The general term of the series was found for a homogeneous ellipsoid of revolution and the first terms of the series were found for some other mass distributions. Here, we have obtained the general term of the series for an arbitrary mass distribution given that the equidensites (surfaces of equal density) are homothetic to the outer surface of the ellipsoid of revolution. Simple estimates and an asymptotics of I _n have also been obtained.     

On the mean value parametrization of natural exponential families — a revisited review

It is well known that any natural exponential family (NEF) is characterized by its variance function on its mean domain, often much simpler than the corresponding generating probability measures. The mean value parametrization appeared to be crucial in some statistical theory, like in generalized linear models, exponential dispersion models and Bayesian framework. The main aim of the paper is to expose the mean value parametrization for possible statistical applications. The paper presents an overview of the mean value parametrization and of the characterization property of the variance function for NEF’s. In particular it introduces the relationships existing between the NEF’s generating measure, Laplace transform and variance function as well as some supplemental results concerning the mean value representation. Some classes of polynomial variance functions are revisited for illustration. The corresponding NEF’s of such classes are generated by counting probabilities on the nonnegative integers and provide Poisson-overdispersed competitors to the homogeneous Poisson distribution.     

Groups with the Weak Maximal Condition on Non-permutable Subgroups

Let G be a group with the weak maximal condition on non-permutable subgroups. We prove that if G is a generalized radical group then G is either quasihamiltonian or a soluble-by-finite minimax group.     

Statistics of the Popularity of Chemical Compounds in Relation to the Non-Target Analysis

The idea of popularity/abundance of chemical compounds is widely used in non-target chemical analysis involving environmental studies. To have a clear quantitative basis for this idea, frequency distributions of chemical compounds over indicators of their popularity/abundance are obtained and discussed. Popularity indicators are the number of information sources, the number of chemical vendors, counts of data records, and other variables assessed from two large databases, namely ChemSpider and PubChem. Distributions are approximated by power functions, special cases of Zipf distributions, which are characteristic of the results of human/social activity. Relatively small group of the most popular compounds has been denoted, conventionally accounting for a few percent (several million) of compounds. These compounds are most often explored in scientific research and are practically used. Accordingly, popular compounds have been taken into account as first analyte candidates for identification in non-target analysis.     

Sensory and Chemical Characteristic of Two Insect Species: Tenebrio molitor and Zophobas morio Larvae Affected by Roasting Processes

The volatile compounds from insects (Tenebrio molitor and Zophobas morio larvae) roasted at 160, 180, or 200 °C and fed with potato starch or blue corn flour were isolated by solid-phase microextraction (SPME), and identified by gas chromatography–mass spectrometry (GC-MS). In the tested material, 48 volatile compounds were determined. Among them, eight are pyrazines, aroma compounds that are formed in food products during thermal processing due to the Maillard reaction. Eleven of the identified compounds influenced the roast, bread, fat, and burnt aromas that are characteristic for traditional baked dishes (meat, potatoes, bread). Most of them are carbonyl compounds and pyrazines. To confirm the contribution of the most important odorants identified, their odor potential activity values (OAVs) and %OAV were calculated. The highest value was noted for isobuthylpyrazine, responsible for roast aroma (%OAV > 90% for samples roasted at lower temperatures), and 2,5-dimethylpyrazine, responsible for burnt aroma (%OAV > 20% for samples roasted at the highest temperature). According to the study, the type of feed did not significantly affect the results of the sensory analysis of roasted insects. The decisive influence was the roasting temperature. The highest scores were achieved for Tenebrio molitor larvae heat-treated at 160 °C.     

Improved Stabilities of Labeling Probes for the Selective Modification of Endogenous Proteins in Living Cells and In Vivo

To date, various affinity-based protein labeling probes have been developed and applied in biological research to modify endogenous proteins in cell lysates and on the cell surface. However, the reactive groups on the labeling probes are also the cause of probe instability and nonselective labeling in a more complex environment, e. g., intracellular and in vivo. Here, we show that labeling probes composed of a sterically stabilized difluorophenyl pivalate can achieve efficient and selective labeling of endogenous proteins on the cell surface, inside living cells and in vivo. As compared with the existing protein labeling probes, probes with the difluorophenyl pivalate exhibit several advantages, including long-term stability in stock solutions, resistance to enzymatic hydrolysis and can be customized easily with diverse fluorophores and protein ligands. With this probe design, endogenous hypoxia biomarker in living cells and nude mice were successfully labeled and validated by in vivo, ex vivo, and immunohistochemistry imaging.     

Thermodynamic Modeling of Nitric Acid Speciation Using eUNIQUAC Activity Coefficient Model

Journal of Solution Chemistry - The speciation of nitric acid was modeled using eUNIQUAC activity coefficient model and the thermodynamic dissociation constant was estimated by solving the...     

Gas-Phase Hydrodechlorination of Chlorobenzene over Alumina-Supported Nickel Catalysts: Effect of Support Structure and Modification with Heteropoly Acid HSiW

Kinetics and Catalysis - The physicochemical and catalytic properties of 6%Ni/Al2O3 catalysts in the gas-phase hydrodechlorination of chlorobenzene (CB) are studied. The catalysts are synthesized...